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Geometry (mander.xyz)

submitted 1 month ago by [email protected] to c/[email protected]

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[–] [email protected] 77 points 1 month ago (18 children)

the point isn't to prove that the triangle is a triangle it's to prove that the system of mathematics you made up actually works

[–] [email protected] 18 points 1 month ago (10 children)

Until you prove that you can't prove that the system you made up works.

[–] [email protected] 3 points 1 month ago (2 children)

Nobody is practically concerned with the "incompleteness" aspect of Gödel's theorems. The unprovable statements are so pathological/contrived that it doesn't appear to suggest any practical statement might be unprovable. Consistency is obviously more important. Sufficiently weak systems may also not be limited by the incompleteness theorems, i.e. they can be proved both complete and consistent.

[–] [email protected] 2 points 1 month ago (1 children)

I think the statement "this system is consistent" is a practical statement that is unprovable in a sufficiently powerful consistent system.

Can you help me understand the tone of your text? To me it sounds kinda hostile as if what you said is some kind of gotcha.

[–] [email protected] 1 points 1 month ago

Just explaining that the limitations of Gödel's theorems are mostly formal in nature. If they are applicable, the more likely case of incompleteness (as opposed to inconsistency) is not really a problem.

[–] [email protected] 2 points 1 month ago (1 children)

Oh, what if the Riemann hypothesis is such a statement then? Or any other mathematical statement. We may not have any use for them now, but as with all things math, they are sometimes useful somewhere unexpected.

[–] [email protected] 1 points 1 month ago (1 children)

It's extremely unlikely given the pathological nature of all known unprovable statements. And those are useless, even to mathematicians.

[–] [email protected] 1 points 1 month ago (1 children)

Math is also used to make a statement/model our universe. And we are still trying to find the theory to unify quantum mechanics and gravity. What if our math is simply inconsistent hence the theory of everything is not possible within the current mathematical framework?

Sure when you are solving the problems it is useless to ponder about it, but it serves as a reminder to also search for other ideas and not outright dismiss any strange new concept for a mathematical system. Or more generally, any logical system that follows a set of axioms. Just look at the history of mathematics itself. How many years before people start to accept that yes imaginary numbers are a thing.

[–] [email protected] 2 points 1 month ago

Dunno what you're trying to say. Yes, if ZFC is inconsistent it would be an issue, but in the unlikely event this is discovered, it would be overwhelmingly probable that a similar set of axioms could be used in a way which is transparent to the vast majority of mathematics. Incompleteness is more likely and less of an issue.

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